Maxima Function
express (expr)
Expands differential operator nouns into expressions in terms of partial derivatives.
express recognizes the operators grad, div, curl, laplacian.
express also expands the cross product ~.
Symbolic derivatives (that is, diff nouns)
in the return value of express may be evaluated by including diff
in the ev function call or command line.
In this context, diff acts as an evfun.
load ("vect") loads this function.
Examples:
(%i1) load ("vect")$ (%i2) grad (x^2 + y^2 + z^2); 2 2 2 (%o2) grad (z + y + x ) (%i3) express (%); d 2 2 2 d 2 2 2 d 2 2 2 (%o3) [-- (z + y + x ), -- (z + y + x ), -- (z + y + x )] dx dy dz (%i4) ev (%, diff); (%o4) [2 x, 2 y, 2 z] (%i5) div ([x^2, y^2, z^2]); 2 2 2 (%o5) div [x , y , z ] (%i6) express (%); d 2 d 2 d 2 (%o6) -- (z ) + -- (y ) + -- (x ) dz dy dx (%i7) ev (%, diff); (%o7) 2 z + 2 y + 2 x (%i8) curl ([x^2, y^2, z^2]); 2 2 2 (%o8) curl [x , y , z ] (%i9) express (%); d 2 d 2 d 2 d 2 d 2 d 2 (%o9) [-- (z ) - -- (y ), -- (x ) - -- (z ), -- (y ) - -- (x )] dy dz dz dx dx dy (%i10) ev (%, diff); (%o10) [0, 0, 0] (%i11) laplacian (x^2 * y^2 * z^2); 2 2 2 (%o11) laplacian (x y z ) (%i12) express (%); 2 2 2 d 2 2 2 d 2 2 2 d 2 2 2 (%o12) --- (x y z ) + --- (x y z ) + --- (x y z ) 2 2 2 dz dy dx (%i13) ev (%, diff); 2 2 2 2 2 2 (%o13) 2 y z + 2 x z + 2 x y (%i14) [a, b, c] ~ [x, y, z]; (%o14) [a, b, c] ~ [x, y, z] (%i15) express (%); (%o15) [b z - c y, c x - a z, a y - b x]